Soliton solutions of some nonlinear evolution equations in shallow water theory

Abstract

This paper proposes some soliton solutions of a generalized Calogero-Bogoyavlenskii-Schiff equation, a (3+1) dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov and a Variant Boussinesq equations. We presented a exponential function method (EFM) for solving the considered evolution equations. The solitary, cuspon and periodic wave solutions are acquired and presented graphically. The soliton solutions of considered equations play a typical role for expressing kinds of wave transmission in any natural instance, particularly in shallow wave kinetics. The results suggest that EFM is effective and useful technique to handle non-linear engineering problems in oceans.